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Terrorism, Insurgency, State Repression, and Cycles of
Violence
Christophe Muller, Pierre Pecher
To cite this version:
Christophe Muller, Pierre Pecher. Terrorism, Insurgency, State Repression, and Cycles of Violence. 2021. �halshs-03134347�
Working Papers / Documents de travail
WP 2021 - Nr 05
Terrorism, Insurgency, State Repression,
and Cycles of Violence
Christophe Muller Pierre Pecher
Terrorism, Insurgency, State Repression,
and Cycles of Violence
∗
Christophe Muller and Pierre Pecher
Aix-Marseille Univ, CNRS, AMSE, Marseille, France.
Contact: christophe.muller@univ-amu.fr and pierre.pecher@univ-amu.fr.
1 February 2021
Abstract
Over the last half century, violent conflicts between ethno-religious organizations and states have shaped the political and economic development context in developing coun-tries. However, global empirical evidence on the dynamic and strategic underpinnings of these phenomena is lacking. Here, we investigate the dynamic violent relationships between the organizations that represent minorities at risk and the governments in Middle-Eastern and North African countries. Our estimates of dynamic panel data mod-els of discrete strategic responses reveal dampened cycles of violence between states and insurgent politico-ethnic organizations due to violent mutual responses. However, such cycles are absent when the organizations target civilians instead, which is more likely after an insurgency spell. Finally, we provide an original game-theoretical inter-pretative framework for our results, which allows us to identify, on average and under sensible restrictions, the Stag Hunt game as an appropriate representation of the (pos-sibly reduced-form) general strategic situations that link states and minority organiza-tions in MENA.This is at odds with the frequent use of the prisoner’s dilemma setting in the literature, or of other ad hoc strategic hypotheses, to analyze conflicts.
JEL Classification: C72, D74, H56.
Keywords: Terrorism, Insurgency, Cycles of Violence, Conflict Theory.
∗This work was supported by French National Research Agency Grants No.CE39-0009-01 and
ANR-17-EURE-0020, funded by the French National Research Agency (ANR) within the framework of the TMENA2 project (http://tmena2.com). We are grateful to participants at several conferences and seminar presentations for their com-ments.
1
Introduction
Over the last half century, ethnic and religious conflicts have shaped the political and economic devel-opment context in developing countries. Like many other regions of the world, the Middle East and North Africa region (MENA) is characterized by antagonism among ethnic and religious groups, with, in each country, long periods of dominance by one group. These political circumstances, where leaders tend to favor their constituency to the detriment of the other factions, create disenfranchised groups that suffer from discrimination (Zussman and Shayo,2011). For example, under the Ba’ath regime, the Shi’i Arabs in Iraq received substantially lower shares of public investment in education, health, and infrastructure than did the other Iraqi ethnic groups.1
This context provides fertile ground for the rise of representative organizations for these discrim-inated populations. Hamas and Hezbollah are instances of organizations that represent Palestinians in Israel and Shi’a in Lebanon, respectively. These organizations fill a political void in deficient demo-cratic contexts and partly respond to the unmet needs of these groups for social services and solidarity mechanisms. They also bolster the political influence of the groups that they represent, which occa-sionally allows them to function as pseudostates running their own police forces and armies.
In these conditions, the recurrent discrimination against these groups may generate violent reac-tions from the organizareac-tions that represent them. Moreover, these organizareac-tions have specific social and political objectives. To achieve them, the organizations may be tempted to use violent strategies. In addition, discrimination by the state may also be enforced using violent means, even when other reasons for state violence may simultaneously exist. For instance, according to the seminal paper by
Crenshaw(1981), the ability of the state to respond repressively to violence is the most critical re-straint on terrorism. In these conditions, the dynamic antagonism between these organizations and the dominant group who controls the state and the army may give rise to cycles of violence. Indeed, asKalyvas(2019) emphasizes, political violence, notably between state and nonstate actors, is almost always interactive and related to the former activities of its target. This is consistent with conflict experience being a much stronger determinant of violent conflict than changes in economic growth, as found byStarr(2010) in Sub-Saharan Africa.
However, once violence has started, it might be asked what allows it to persist since it is costly to both sides.2 This raises questions on the origin of violent strategies by organizations or by the state,
1Thus, these populations are not always stricto sensu minorities but rather groups discriminated against by the state.
The term ‘minority’ should be interpreted here in the sense of the ‘Minorities at Risk’ database that we use, that is, politically
significant communal groups, who collectively suffer or benefit from systematic discriminatory treatment at the hands of other societal groups. In 1987, 75-80 percent of the population in Iraq was Arab, i.e., 24 million people, of whom 15 million were Shi’a, 9
million were Sunni, 15 percent were Kurds (4 million people) and 5 percent belonged to other groups.
2Diverse conjectures have been proposed in the literature. For instance,Peffley, Hutchison, and Shamir(2015) show
that terrorism in the Israel-Palestine conflict has reduced the political tolerance of the Israeli, which may diminish the chances for a return to peace. See also the theoretical explanations for violence escalation ofAcemoglu and Wolitzky (2014),Berman and Laitin(2008), andBesley and Persson(2011).
which may often be perceived as responses to former violence from their opponent. Thus, one poten-tial explanation for violence is that it arises from violent mutual responses that engender a violent and stable strategic equilibrium.
This is the question we study in this paper, first, by using information on sequences of lethal vi-olence by these organizations and by the state contained in the Minorities at Risk Organizational Be-havior dataset (MAROB,Wilkenfeld, Asal, and Pate,2011) and second, by proposing a new method for identifying parsimonious game structures in dynamic systems of conflict responses.
Our approach is based on the popular use of game theory to describe violent relationships be-tween states and rebel or terrorist groups. Many authors have described violent strategic interactions by relying on more or less basic game theory.3 Thus, this paper belongs to a relatively small mixed theoretical and empirical literature that studies the political and economic causes and consequences of violence and its strategic roots.4More specific to our interests,Bueno de Mesquita(2013) andCarter (2015,2016) study theoretically the strategic choice between terrorism and insurgency and show that this choice can be strategically and dynamically linked to expectations of a violent state response.5
On that account, beyond our focus on strategies as responses to violence, an interesting issue lies in the dynamic pattern of organization-specific violent strategies, notably the choice between civil-ian and military victims, i.e., terrorism versus insurgency.6 This is a common theme in the conflict literature. Berman(2009) claims that “The failed insurgents of today often become the terrorists of
tomor-row”(p.160).Bloom(2005) contends that terrorism is used by nonstate actors only after other strategies
have failed. One reason for this is the hardening of military targets, which makes attacks on civilians comparatively easier.7 Using a country-level approach,Enders and Sandler(1993) estimate a vector
3For example, recently:Acemoglu and Wolitzky(2014),Azam and Hoeffler(2002),Baliga and Sjöström(2012),Berman,
Shapiro, and Felter(2011),Carter(2015),Enders and Sandler(1995),Jacobson and Kaplan(2007), andSiqueira and Sandler (2006).
4SeeGaibulloev and Sandler(2019) for a review.
5Bueno de Mesquita(2013) features a model of rebel tactical choice between insurgency, terrorism, and peace, with
en-dogenous mobilization under uncertain rebel capacity and economic outside options for the population. By studying these tactics jointly, he shows that terrorism is stimulated by intermediate economic opportunities and that counterinsurgency may lead to terrorism when rebel fighting capacity is low. Carter(2016)’s approach is based on subgame perfect Nash equilibria in sequential games. His model explains the tactical choice of organizations between insurgency and terrorism, with an emphasis on the state’s response. Insurgency can be used to provoke violent responses by the state to harness grievances and generate support from the population. In contrast, terrorism can prevent violent responses by the state. In both cases, these hypotheses are consistent with our empirical results at the organization-year level and those ofCarter (2016) from a tentative static multinomial logit estimate using Western European data on terror attacks. Carter(2015) provides another theoretical explanation for the choice between insurgency and terrorism based on the possible gains in territory control entailed by insurgency, which involves the future ability to extract resources. Carter claims that the states most capable of fighting territorial opponents face a higher risk of terrorism as an alternative strategy to insurgency.
6Condra, Long, Shaver, and Wright(2018),Fortna(2015),Gould and Klor(2010), andKis-Katos, Liebert, and Schulze
(2014) argue and empirically support that each of these tactics can achieve a certain degree of success, which varies with the logistics needed, the risks, the likelihood of a favorable outcome, and the consequences for the image of the organization.
7In contrast, vanguard violence is a potential mechanism for the transition from terrorism to insurgency, meant to
autoregression (VAR) model that partly explains the type of attack with the installation of metal de-tectors and embassy fortification. In this case, transitions between insurgency and terrorism can be interpreted as substitutions due to a change in the relative shadow prices of the two options. Our dy-namic empirical framework allows us to detect such shifts between strategies. Terror cycles have also been studied from a pure theoretical viewpoint (Faria, 2003; Das, 2008), which also invites dynamic empirical modeling. Of course, details about individual strategies, for example, by political leaders or militants, should be probed by using microeconomic data on individuals, which is not our vantage point here.
The distinction between terrorism, insurgency, and state violence is essential. In particular, dy-namic patterns may be specific to each category of violence and its specific objectives. For instance, rebels may have direct goals, such as the destruction of essential targets or the control of assets and territories. In contrast, the purpose of terrorism may be indirect, such as instilling fear and chang-ing some incentives of the targeted audience.8 These goals can sometimes be attained through latent threats without actually engaging in violence. Likewise, the optimal response by the state may depend on the chosen strategy of its opponent because the state’s response hangs on its capacity to precisely identify the perpetrators of violence or on its anticipation of retaliation by the adversary.9
This study addresses these questions by investigating violent dynamic responses between organi-zations representing minorities at risk and the government in MENA countries. To do this, we estimate dynamic panel data models of the violent responses of organizations and governments and exhibit the relative prevalence of these responses. Violent responses must be apprehended as likelihoods rather than systematic reactions. We find that latent violent responses occur in approximately one-fifth of cases. Moreover, the estimation results are consistent with dampened cycles of violence between the central state and insurgent politico-ethnic organizations. However, when organizations turn to terror-ism instead of insurrection, they are no longer found to respond significantly to state violence. Finally, we find that organizations are more likely to engage in terrorism a few years after an insurgency spell. Our research relates to a small empirical literature about terrorism as violent responses to vio-lence, initiated byBrophy-Baermann and Conybeare(1994), who find that the aggregate time series of terrorist attacks and government reprisals in Israel from 1968 to 1989 support the efficiency of a fixed retaliation rule by governments. Jaeger and Paserman(2006,2008) estimate violent responses using daily information on fatalities on both the Israeli and Palestinian sides during the 2000-2004 Second Intifada. These authors estimate VAR specifications that link the number and incidence of deaths to past values of own and opposing-side fatalities. On the one hand, they find a positive and significant
8For instance,Gould and Klor(2010) highlight the existence of a concave relationship between local terrorist events in
Israel and the propensity to grant territorial concessions to Palestinians, as measured by surveys.
9Sometimes too strong a use of force by one side triggers increased radicalization, popular grievances, or justifications
for violence. The presence of such backlash effects favors provocation strategies. As pointed out by diverse authors such asArce and Sandler(2010),Bueno de Mesquita and Dickson(2007),Condra et al.(2018), andJacobson and Kaplan(2007), an organization may stage a terrorist attack to enhance its popularity as a consequence of the expected abusive response of the state.
reaction of Israel to casualties caused by Palestinians. On the other hand, they do not find evidence of a substantial response from the Palestinian faction.Jaeger and Paserman(2009) offer refined estimates of Israeli and Palestinian violent reactions over two weeks by focusing on targeted killings of leaders and suicide attacks. Although they do not use any formal game model, they reject ‘Tit-for-Tat’ in that case. Durante and Zhuravskaya(2018) confirm the results ofJaeger and Paserman (2008), although with significant responses from the Palestinians in some instances, and show that news pressure in United States affects the timing of the attacks by the Israeli Defense Forces.10 Bejan and Parkin(2015), who estimate a VAR model of repressive and conciliatory actions by the Israeli government and of terrorist attacks, find that government actions have a deterrent effect. However, beyond the rather special Israel case, there has been no similar empirical investigation for other countries of the MENA area, let alone for a broad sample of MENA countries together. This paper is the first systematic and global investigation of the violent dynamic interactions of the central states with discriminated mi-nority groups in MENA countries. Finally, by focusing on MENA, we avert the inclusion of irrelevant cases such as regions with rare minorities or no violence at all.
A virtue of adopting a global approach to all MENA countries is that we thereby avoid some com-mon pitfalls in conflict studies. First, we eschew the focus on special, although interesting, country cases that may promote a distorted picture of the general phenomena of conflict between states and minorities. In particular, violent contexts may be overrepresented in conflict studies. This may give rise to selectivity bias at the country and minority group levels. Second, by focusing on the MENA region, we ensure a certain homogeneity of geographical and historical backgrounds, which limits the influence of uncontrollable specificities in the analysis.
As a starting point for our empirical investigation, we build on the literature on terrorist organi-zation violence that uses the MAROB database, such asAbrahms and Potter(2015) andAsal, Brown, and Dalton(2012).11 In these studies, however, the inference rests on the cross-organization variation, neglecting the essential information contained in the panel structure of the data. In particular, this matter not only raises common concerns about the estimation, such as omitted variable bias due to the circumstances of countries in certain years and reverse causality, but also prevents direct investigation of dynamic responses by the state or the organizations. We fill this gap.
In contrast with this literature, our empirical approach relies on numerous strategic pairs obtained by matching central MENA states with each organization representing a discriminated group from the
10In agreement withDurante and Zhuravskaya(2018),Asali, Abu-Qarn, and Beenstock(2017) find some evidence of a
response by the Palestinians using nonlinear estimation techniques.
11Abrahms and Potter(2015) argue that a lack of strong leadership is a decisive element in the use of terrorism. Asal
et al.(2012) study the role of the lack of strong leadership in organizational splits, which is assumed to be a step towards the use of violence because splinter groups are less peaceful. Asal, Schulzke, and Pate(2017) concentrate on the use of force and find that organizations that support the exclusion of women from public life and changes in state boundaries and those suffering from state repression are more likely to use violence. In the same vein,Asal, Conrad, and White(2014) show a link between diaspora support and political activities abroad.Conrad and Greene(2015) observe that a multiplicity of organizations in a country correlates with relatively more shocking attacks. Additionally,Asal and Wilkenfeld(2013) note the association between gender inclusiveness and nonviolence.
corresponding country. Preliminary data examinations with transition matrices suggest that current violence may often originate in past violence, from the agent and from its adversary. This setting allows us to control for, on the one hand, a broad range of unobserved fixed and year-specific char-acteristics at the state×year level, such as civil wars, economic development, the national political conjuncture and other social indicators, and, on the other hand, at the organization level, fixed fac-tors such as its primary type of grievance, religious character, size, or relevant ethnic minority.12
The second contribution of this paper is to propose a new method for associating a strategic in-terpretation with dynamic systems of adverse strategies among opponents. Indeed, a strategic frame-work is necessary to support an interpretation of the estimated dynamic coefficients in terms of ‘strategic responses’ and to avoid confusing it with other kinds of joint dynamic changes in the op-ponent’s strategies. This new method is also important because most interpretations of estimates in the literature, notably in the violent conflict literature, are in terms of a priori narratives involving strategic games that include typically unobservable and unidentifiable features, such as beliefs, antic-ipations, and timing rules. In that case, in the interpretation, it is impossible to separate what comes out of the data from what flows out of the fertile and ingenious imaginations, and sometimes personal convictions, of the researchers. In most empirical cases, only parsimonious game structures should be identifiable.
We deal with this issue by restricting the strategic model to the strategic forms of the game, deliber-ately stripped down from any other model specification hypotheses. Then, in normal forms, we exploit the information about, first, the location of the Nash equilibrium and, second, the moves consistent with the payoff matrix. As an identification restriction, we associate these two pieces of information with long-term and short-term dynamic responses.
This method leads us to examine the complete class of two-by-two simple strategic forms and iden-tifies the types of games that are consistent with the estimation results of the dynamic system of vi-olent strategies by the state and the organizations. We find that the only game that can satisfactorily represent, on average, the observed conflicts between states and organizations is the Stag Hunt game, invented by Jean-Jacques Rousseau in the XVIIIthcentury. This finding allows us to draw policy
con-clusions, not only in terms of the characteristics of the Stag Hunt game but also in terms of policies fostering shifts to another type of game structure.
The rest of the paper is organized as follows. Section 2 presents the data. Section 3 displays the empirical model and discusses the associated econometric issues. The baseline results and a few ro-bustness checks are reported and analyzed in Section 4. In Section 5, we confront the empirical results with a novel analytical framework, which yields a unique one-shot game representation of the average conflict situation considered. We identify policy recommendations. Finally, Section 6 concludes.
12Including available information on external funding and on the provision of social services by organizations has been
attempted, but it has no significant effect in these data, and we do not pursue this research line here. Note that this result does not contradict the violence-depleting effect of service provision found in Iraq byBerman et al.(2011), since in their case, it is the government that provides the services, not the organizations.
2
The Data
2.1
Source
Our primary data source is the Minorities at Risk Organizational Behavior database (MAROB,Wilkenfeld et al.,2011), accessed through the National Consortium for the Study of Terrorism and Responses to Terrorism, which is a Department of the Homeland Security Center of Excellence, at the University of Maryland.13 It provides us with information on 112 organizations, which represent ethnic ‘minorities’ in 12 Middle Eastern or Northern African countries for 25 years between 1980 and 2004. This period is particularly relevant, as it corresponds to major political events in the region, such as the 1979 Iranian Islamic Revolution, the 1980 Turkish military coup, the US-led coalition invasion of Iraq in 2003, and the end of the Al-Aqsa Intifada in 2004/2005.
The surveyed organizations claim to represent the interests of ethnic minorities or discriminated groups, have political goals, and have been active for at least three years.Piazza(2011) finds that coun-tries that economically discriminate against minorities suffer terrorist attacks more frequently than countries that do not discriminate against these groups or do not have such groups. These organiza-tions use violent as well as non-violent strategies, such as education programs, propaganda campaigns, and electoral politics. Their average life span is 15.74 years, with a median of 17 years. A total of 33 organizations were active violently or non-violently throughout the whole period, representing 29 percent of the total.
We construct our estimation dataset by extracting the variables ‘STATEVIOLENCE’, ‘ORGST7’, and ‘ORGST8’ from the MAROB database. ‘STATEVIOLENCE’ records information on lethal violence by the state, while ‘ORGST7’ and ‘ORGST8’ provide information on terrorism, i.e., lethal violence targeting civilians, and insurgency, i.e., lethal violence targeting the military or police, by the organization, respectively. We recode these variables as binary indicators equal to zero for ‘No use of violence’ and one for ‘Use of violence’. Details on the construction of the variables are provided inAppendix.
2.2
Descriptive statistics
The descriptive statistics inTable Idisplay considerable variation across countries, periods, and or-ganizations in terms of patterns of violence. This justifies the crucial introduction of country×year fixed effects in our econometric specifications to control for factors that may lead to these differ-ences. Specifically, violence is concentrated in certain periods and countries, such as Israel and Iraq. In contrast, the most typical situation is the absence of violence. Our econometric identification and estimation strategy, which essentially exploits the transitions between nonviolence and violence, suc-cessfully surmounts the challenge imposed by the amount of variability in the data.
13Available from https://dataverse.harvard.edu/dataset.xhtml?persistentId=hdl:1902.1/15973&
After discarding the few observations with missing information for our main variables, we end up with a sample of 1,732 observations that can be indexed by state-organization pairs and years.14 In the FE estimations, two organizations are dropped from the estimation because of missing values. The final baseline sample contains 110 organizations. Overall, terrorism occurred in 13.6 percent of the cases, insurgency in 9 percent, and state violence in 13.3 percent. Cyprus and Bahrain did not experience any violence. Apart from these two countries and still focusing on minority-related conflicts, Algeria and Iran had no terrorism; Algeria, Syria, Jordan, and Saudi Arabia, no insurgency; and Saudi Arabia, no state violence. Terrorism is more frequent in Turkey and Israel (29.8 and 26.2 percent, respectively), insurgency in Turkey and Iran (42.1 and 28.8 percent, respectively) and state violence in Turkey and Iran (50.9 and 42.4 percent, respectively).15
Data inspection reveals that violence spans do not last long in general. The longest violent conflicts involve the relationships between the Palestinian Islamic Jihad and Israel, Hamas and Israel, the South Lebanon Army and Lebanon, the Partiya Karkari Kurdistan (PKK) and Turkey, and the Patriotic Union of Kurdistan (PUK) and Iraq, which lasted between 17 and 25 consecutive years. Apart from these five organization-state pairs, the violence spans are shorter than ten years, with a median below four years. In addition, some organizations are always non-violent.16
The transition matrices across years for each violent strategy inTable II show that even though violence exhibits a certain degree of persistence, there is a general tendency to return to peace. Vio-lence is transitory, and our model helps us to analyze the likelihood of a return to peace. For instance, from Panels (a) to (c), the probability of a return to peace in the next year is 68 percent from a situation of terrorism, 78 percent from insurgency, and 72 percent from state violence. Table IIIdisplays non-parametric estimates of conditional frequencies that provide hints about potential violent responses to violence. These estimates have the advantage of being independent of the theoretical models and of the empirical models used. They are also consistent with the literature that often uses this kind of direct criterion as evidence for strategic responses to violence. However, they remain relatively raw diagnoses that do not control for covariates or richer dynamic effects.
Panel (a) of the table shows the frequency with which the organizations are observed at different terrorism levels (none, minor, major), given that the state was violent or not against the organization in the former year. Obviously, the level of terrorism increases with former state violence. Nine-tenths of the organizations observed as having enjoyed a non-violent state in the previous year refrain from
14These variables include the category ‘Missing value or no basis for judgment’, for which we have dropped the
corre-sponding observations. This trimming removes 57 observations out of a total of 1,789 (3.2 percent) for 19 different organi-zations that are kept in the sample for the other valid observations. These missing values are consecutive and concentrated among a few Iraqi organizations.
15Recall that, as mentioned above, these data only capture violence involving ‘minorities’ as defined by MAROB. In
par-ticular, the ‘Black decade’ of the nineties in Algeria is not covered, as it concerned Islamic militants not characterized by minority status.
16For example, the Democratic Party (Turkish Cypriots, Turkey), the Popular Movement (Berbers, Morocco), the United
Azerbaijan Movement (Azerbaijanis, Iran), the National Liberation Party (Maronite Christians, Lebanon), and the Bahrain Freedom Movement (Shi’a, Bahrain).
relying on terror strategies. However, when confronted with state violence instead, almost one-fourth use minor terror strategies, and 13 percent use major terror strategies. In the other panels, (b) to (d), similar suggestive patterns of seemingly violent responses to violence can be observed for the other pairs of violence variables shown in the table, that is, insurgency given former state violence, state violence given former terror, and state violence given former insurgency. In all cases, a positive first-order stochastic dominance relationship can be observed between the adversary’s violence in the previous year and the contemporary violence of the agent. This result suggests that models of violent strategic responses may fit the data well.
Table IVandFigure Icontain basic information about the strategy profiles for 15 organizations, which is used later to illustrate the main mechanisms discussed in this paper.17
In addition to this, MAROB data provide information on several organizational features that vary little over time, such as education, propaganda activities, the representation of the group, its political orientation towards officials and electoral politics, solicitation of external support, and non-coercive or forceful solicitations of local support. MAROB data also provide information on fixed characteris-tics, such as the openness, legality, militancy, and types of grievances of the organization. We do not use these fixed or quasi-fixed variables because our fixed-effect specification already takes them into account.
3
The Empirical Model and the Estimators
The empirical model describes the fixed and dynamic determinants of terrorism, insurgency and state violence for each state-organization pair. Thus, as pointed out byShapiro(2012), terrorism is consid-ered to be one tactical option among several for opposition groups, which improves the credibility of tests of strategic explanations. To allow for an autonomous treatment and distinct samples with spe-cific missing values of independent and dependent variables, we specify and estimate each strategy-specific equation separately. The autoregressive terms are viewed as expressing the inherent inertia present in many violent processes. The terms describing the lagged strategies of the opponent are the main interests, as they reveal information about strategic responses. Finally, the second strategy of each organization, i.e., terrorism or insurgency, is included as a regressor in the equation for its other strategy because we want to explore transitions between these two strategies.18 The tests conducted, as discussed below, lead us to favor a two-year lagged specification for the lagged independent and autoregressive variables. Note that the strategic interpretation of these equations is not symmetric since, first, the state violence equation does not include an alternative strategy, and, second, the state faces several organizations while each organization belongs to a unique state.
17Figure A1 in the Online Appendix extendsFigure Ito all violent organization-state pairs.
18Bueno de Mesquita(2013) andEnders and Sandler(1993) emphasize the importance of studying these tactics jointly,
We begin our analysis by considering the determinants of terrorism by an organization in the fol-lowing linear autoregressive specification:
Terrorismi,t = 2 X j=1 α1jTerrorismi,t−j+ 2 X j=1 β1jInsurgencyi,t−j (1) + 2 X j=1
γ1jState Violencei,t−j+ ζ1i + δ 1
c(i),t+ 1 i,t,
where the subscript i stands for organization-state pairs (or organizations since the state is uniquely determined by the identity of the organization). We include two lags of the dependent variable Terrorismi,t−j with j = 1, 2 (a dummy variable for the occurrence of lethal terrorist attacks by
or-ganization i in year t − j) to capture the persistence of violence. Our main coefficients of interest in this equation are the coefficients on the two lags of State Violencei,t−j with j = 1, 2 (a dummy
variable for the occurrence of lethal state violence against organization i in year t − j). The two lags of the variable Insurgencyi,t−j with j = 1, 2 (a dummy variable for the occurrence of lethal insur-gency actions by organization i in year t − j) can alternatively be considered mere controls. The ζ1
is
are organization fixed effects, and the δ1
c(i),ts are country×year fixed effects, with c(i) denoting the
country of organization i. The inclusion of all these fixed effects should attenuate any possible omitted variable bias. In this respect, country-year fixed effects are essential because they incorporate a large number of observed and unobserved country-specific conjuncture factors, such as GDP per capita and the general circumstances in neighboring countries. Organization-specific fixed effects, ζ1
i, allow us
to control not only for the myriad fixed characteristics of each organization but also for many of its strategies that are often stable over time, such as being involved in local service provision.
Similarly, we specify the following equation for the organization strategy ‘Insurgency’: Insurgencyi,t = 2 X j=1 α2jTerrorismi,t−j+ 2 X j=1 β2jInsurgencyi,t−j (2) + 2 X j=1
γ2jState Violencei,t−j+ ζ2i + δ 2
c(i),t+ 2 i,t,
again with organization and country×year fixed effects (ζ2
i and δ2c(i),t, respectively). Finally, to
in-vestigate the response of the state to violence from the organizations, we specify a comparable linear equation:
State Violencei,t = 2 X j=1 α3jTerrorismi,t−j+ 2 X j=1 β3jInsurgencyi,t−j (3) + 2 X j=1
γ3jState Violencei,t−j+ ζ3i + δ 3
c(i),t+ 3 i,t,
where the two lags of the dependent variable capture the inertia in State Violence. Here, the lags of the explanatory variables Terrorism and Insurgency describe the strategies of the organization to which the state may respond. In all these equations, αk
j, βkj,and γkj are parameters to be estimated. The kjs
are error terms subject to suitable semiparametric restrictions that are discussed below. Under these specifications and without accounting for equation-specific missing values, the system of equations is akin to a VAR model of order two, augmented with relevant fixed effects.
We first use a fixed-effect estimation technique, which requires strict exogeneity assumptions for the error terms, i.e.,
E[ki,t|Yi,t−1k , Yi,t−2k , Xi,t−1k , Xki,t−2, ζki, δkc(i),t] = 0 (4) for all i and t, and k = 1, 2, 3, where Yk
i,tis the dependent variable in equation k for organization i and
year t and Xk
i,tis the vector of nonfixed explanatory variables in equation k for organization i and year
t. Note that this conditioning includes two distinct types of fixed effects as opposed to the condition for within-group estimators. Under the stated assumptions, not only is this estimator consistent when the number of organizations N goes to infinity, but it is also consistent when the number of periods T goes to infinity while N is fixed (Arellano,2003). Therefore, we benefit from the non-negligible number of years (25) over which the organizations are followed. These fixed-effect estimations are informative regarding dynamic partial correlations among the violence variables even if, because of the presence of the lagged dependent variable, the strict-exogeneity restriction may not be satisfied, for example, if some error terms are serially correlated.
As a reply, not only to this issue but also to the possible endogeneity bias perhaps resulting from reverse causality and omitted variables, we also make use of a first-differenced generalized method of moments (DGMM), which yields our preferred estimations. For this, we first demean the variables from their country-year mean. In other words, we regress the variables Terrorism, Insurgency, and State Violence on the full set of country×year dummy variables and compute the residuals of these estimations. Then, the residualized data are further transformed into first differences to eliminate the organization fixed effects.
Such preliminary purging of effects, especially for fixed effects, is common in econometrics.19 We
follow this approach for the DGMM because it simplifies the estimation procedure. However, this im-plies neglecting the potential correction of the estimates of the dynamic coefficients by simultane-ously estimating the country×year fixed effects. The trade-off is that this approach allows for deci-sive simplification of an otherwise numerically intractable optimization estimation problem, which involves not only many local optima but also non-differentiabilities and discontinuities due to the presence of dummy variables associated with the fixed effects. Nevertheless, GMM estimation results can still be obtained by directly estimating all the effects together, including the organization-specific fixed effects and country×year fixed effects, provided that the most insignificant fixed effects ob-tained in the previous procedure are dropped from the model.20 Finally, the approach also greatly simplifies the estimation of the asymptotic standard errors of the DGMM. Even so, bootstrapped stan-dard errors are also estimated, clustered by organization, and provide accurate estimates that are very close to those obtained with the asymptotic estimations of standard errors, which is reassuring.21
For the implementation of the DGMM, the error term of the first-differenced equation is assumed to be orthogonal to the instrument matrix of the lagged explanatory variables in levels, limited to lags two to four.22 Specifically, we assume the moment conditions
E[∆kitYi,t−sk ] = 0and E[∆k itX
k
i,t−s] = 0 (5)
for k = 1, 2, 3, t = 1, . . . , T and s = 2, 3, 4, which are the basis of the GMM estimations, where ∆is the first difference operator and here Y and X denote the variables in terms of deviations from the country-year mean. We trim the instrument set to a maximum of four-year lags to avoid instru-ment proliferation and the degradation of the small-sample properties. In addition, we collapse the instruments for different periods to reduce the instrument count and avoid overfitting the dependent variable, which may lead to a failure to remove its endogenous component, as discussed inRoodman
(2009). In this regard, the results of the Hansen overidentification test support that the instrumen-tation avoids overfitting, with p-values from 0.11 to 0.53 inTable V. Using second-order and higher lags as the instruments is standard, and furthermore, it is supported by the results of the AR(2) tests, which do not reject the absence of second-order correlation in the differenced error terms at the five percent level, with p-values from 0.081 to 0.54, as shown inTable V.23
This approach avoids the pitfalls associated with simultaneity on two grounds. First, as the equa-tion does not contain regressors contemporaneous to the dependent variable, all effects that may hap-pen during a year cannot directly generate simultaneity bias. Second, the right-hand side variables
20Specifically, we have checked that the DGMM results are identical to those obtained by simultaneously estimating
the country×year fixed effects, limited to those that are significant at least at the 10 percent level in the FE estimation. Therefore, the preliminary purging of effects seems to be innocuous.
21The bootstrapped standard errors are obtained via 1,000 bootstrap replications with stratification at the country level.
That is, each bootstrap sample has the same number of organizations per country as the original sample.
22We trim the sample by dropping the eight organizations with too few periods due to the need for lagged variables in
the difference GMM (DGMM)estimations.
that could be correlated with omitted contemporaneous regressors are all instrumented in the DGMM estimations. However, if they had been included, the contemporary effect could have been substituted to yield a VAR-type system of equations. Then, an alternative interpretation of System (1)-(2)-(3) is that it is a reduced-form specification possibly incorporating some instantaneous strategic responses. Alternatively, contemporary effects could be included in only one equation of the system while ex-cluding them from the other two equations. For example, one could assume that the state would have the capacity and means to give almost immediate responses, whereas the organizations would require more time for internal collective decision making and capacity building before launching an insur-rection or a terrorist campaign. In that case, only the state violence equation would be considered to be in reduced form, while the insurrection and terrorism equations would retain their structural interpretation.
Subsequently, we also use these residualized data to estimate fixed-effects panel VAR models based on jointly estimating the parameters of equations (1) to (3).24However, because of the stronger orthog-onality conditions necessary in the case of the panel VAR, we prefer to keep the previous estimations as our baseline. In addition, the panel VAR estimations yield similar results.
4
Results
Table V contains our baseline results. The fixed-effect estimates are shown in the odd-numbered columns, and the difference GMM estimates are shown in the even-numbered columns. The proxim-ity of the fixed-effect and DGMM results regarding the magnitude and significance of the coefficients may be an indication that endogeneity issues do not overly contaminate the equations estimated with these data. All columns contain a full set of country×year fixed effects, which are estimated for the fixed-effect estimator columns (1, 3, 5), while they are differenced out for the DGMM columns (2, 4, 6). Asymptotic robust standard errors are displayed in parentheses. For the DGMM estimations, boot-strapped standard errors are displayed in brackets. In practice, significance tests using any of the standard error estimators give the same inference results in our baseline specification.
4.1
The terrorism equation
Columns 1 and 2 display the FE and DGMM estimates of Equation (1), respectively, where the depen-dent variable is Terrorism by organization i and year t. The autocorrelation coefficient of the variable Terrorism is precisely and closely estimated with the two methods (0.2226 with FE and 0.1984 with DGMM). Clearly, there is a nonnegligible degree of persistence in terrorism beyond the persistence already accounted for by the fixed effects, while it is far from dominating the other effects. The
ficients for the second-order autocorrelation are also positive, although insignificant at conventional levels.25
A consistent finding concerns the coefficient on the variable Insurgencyt−2, which is estimated at 0.12 for FE and 0.15 for DGMM and is significant at the five percent level. Namely, given the general tendency of an organization and of other organizations in the same country and same year to use terrorism, as captured by the fixed effects, it is more likely that this organization will use terrorism if it had been engaged in insurgency two years earlier. The estimated FE coefficient on the variable Insurgencyt−2 in Column 1, which is 0.1175, implies that a one-time change from no insurgency to insurgency by an organization generates an approximately twelve percent increase in the probability of engaging in terrorism two years later. This is consistent with the rebel tactics analyzed inBueno de Mesquita(2013).
The coefficients for the response of terrorism to state violence, although insignificant in the fixed-effect estimation, are slightly significant in the DGMM estimates for ‘State Violence’ at t-1 and t-2, albeit negatively. This negative sign may hint at the eradication of terrorist groups by violent state repression or at least the degradation of the capability of the violent organization, thus preventing further attacks or deterring attacks. In that case, the estimated effects may reveal direct damages inflicted by state violence rather than deliberate strategic responses by the organizations. The fragility of the terrorism response to state violence may also be related to terrorism being popular and efficient when limited, but not any more above a threshold level, at which point the targeted populations may harden their stance (Gould and Klor,2010).
Some organizations included inFigure Ihave a strategy time profile that suggests a transition from insurgency to terrorism. For example, this is the case for the Supreme Council for the Islamic Revolu-tion in Iraq and its military wing the Badr Brigade (Shi’a, Iraq) and for the Popular Front for the Lib-eration of Palestine–General Command (Palestinians, Lebanon), led by Ahmed Jibril, a splinter group from the PFLP more focused on military action. A comparable pattern is also noticeable with Amal (Shi’a, Lebanon).
4.2
The insurgency equation
Columns 3 and 4 show the estimation results for insurgency equation (2) based on the FE and DGMM estimators, respectively. Both estimates of the first-order autocorrelation coefficient are substantial and highly significant (0.41 for the FE estimation, 0.49 for the DGMM estimation), approximately twice the magnitude of the corresponding coefficient in the terrorism equation. Once insurrection is sup-ported by an organization, it is likely to last for several years.
Unlike the previous equation, we observe a positive and significant coefficient on the response
25However, terrorism rapidly fades away in general, as in the cases of the Progressive Socialist Party (Druze, Lebanon)
of insurgency to state violence in the fixed-effect estimates equal to 0.076 and equal to 0.122 with DGMM. An organization is therefore more likely to use insurrectional violence against the military and the police forces if the state targeted it violently in the previous year. The FE estimate implies that a one-time occurrence of state violence sparks a 7.6 percent rise in the probability of insurgency the next year, everything else equal. Assuming a permanent change, dividing the sum of the short-run coefficients by the adjustment for the AR(1) and (2) coefficients yields a long-short-run increase of 15.2 percent.26
Therefore, the results indicate a definitive insurgency response to state violence. The history pro-files, displayed in Figure I, of the Kurdistan Socialist Democratic Party (Kurds in Iraq) and Hizb al Da’wa al-Islamiyya (Shi’a in Iraq) are consistent with this mechanism. This is also the case for the Islamic Da’wa Party founded in 1958, which is one of the main two Shi’a parties in Iraq, along with the Supreme Council. This party supported the Iranian revolution and received funding and assistance from Ayatollah Khomeini in return. All its members were sentenced to death by the Ba’ath regime of Iraq. Later, they attempted to kill Saddam Hussein in 1982 in Dujail, which resulted in fierce repression by Hussein’s regime with approximately 145 fatalities.
4.3
The state violence equation
Finally, in columns 5 and 6, we consider the violent response of the state against any organization i in the same country in year t, according to equation (3). The pattern of the estimated coefficients resem-bles that in the previous two columns. First, state violence exhibits a certain degree of persistence. The AR(1) coefficient is positive and significant at the one percent level in both equations, with an estimated value of 0.19 in the fixed-effect estimation in Column 5 and of 0.27 in the DGMM estimation in Column 6. There is also a strong tendency for the state to respond to insurgency led by the organi-zation, as shown by the positive and significant coefficients on the lagged Insurgency variables (0.17 and 0.23 for the FE and DGMM, respectively).
These findings indicate an asymmetric situation, where the state responds more vigorously to vi-olence than organizations do, perhaps because it is stronger and has a greater ability to act militarily. We also consistently find a limited positive strategic response to terrorism, with smaller coefficients of 0.055 and 0.064, respectively, which are only significant at the 10 percent level in the fixed-effect equation and are insignificant at conventional levels in the DGMM equation. Less systematic state responses in that case may stem from the nature of terrorist actions, which sometimes mask their perpetrators, who are therefore harder to target.
The FE coefficient estimate of the lagged Insurgency variable in Column 5, which is 0.1699, implies that a one-time occurrence of insurgency generates a 17 percent rise in the probability of state
vi-26In Column 4, we further restrict the lag length of the instruments to s = 2, 3 for the sake of the Hansen instrument
olence the next year, everything else equal. Assuming a permanent change, by dividing the sum of the short-run coefficients by the adjustment for the AR(1) and (2) coefficients, we obtain a long-run increase of 19.6 percent. Therefore, there are substantial responses from states to insurgency. Some of the observed strategy profiles inFigure Iare consistent with this mechanism, such as that for The Organization of the Revolutionary Toilers of Iranian Kurdistan, which was involved in the Kurdish re-bellion in Iran, and that for the Kurdish Democratic Party of Iran. Finally, it is plausible that part of the response of the state could be almost immediate within the same year and would therefore escape the estimation. Such occurrence should reinforce the magnitude of the estimated responses, which therefore can be seen as a lower bound.
In addition, considering equations (1), (2), and (3) as a joint dynamic system may provide addi-tional insights into the dynamic properties of this system, which depend on the eigenvalues of the corresponding transition matrix. The matrix of the stacked coefficients for the estimated dynamic system (FE estimates in columns 1, 3, and 5) has six eigenvalues with complex moduli of 0.4958, 0.2668 (twice), 0.1139 (twice), and 0.1095. For the DGMM estimates in columns 2, 4, and 6, the corresponding moduli are 0.6481, 0.3514 (twice), 0.1833 (twice), and 0.1578, respectively. As these eigenvalues are all inside the unit circle, the system converges to a unique steady state determined by the fixed effects.
4.4
Panel VAR estimates and impulse response functions
Table VIcontains our fixed-effect panel VAR estimates of equations (1) to (3), computed using the esti-mator ofHoltz-Eakin, Newey, and Rosen(1988).27 A potential advantage of simultaneously estimating all equations is the efficiency gain stemming from accounting for correlations among the errors of the different equations. However, the sample must be truncated to 1,373 observations because of miss-ing values. Nevertheless, the estimated panel VAR is useful for estimatmiss-ing impulse response functions easily. In addition, the country×year fixed effects are again taken into account through prefiltering.
Columns 1 to 3 display the estimates of the exactly identified system when lags 1 to 2 are used as instruments. Columns 4 to 6 display the corresponding results with lags 1 to 3. We obtain results similar to those in the previous subsections in terms of the sign, magnitude and significance of the main coefficients.
In particular, in the terrorism response equation, the coefficient on Insurgencyt−2 is significant at the five percent level (value of 0.163 in Column 1 and 0.133 in Column 4), and the coefficient on State Violencet−1is negative— -0.131 and -0.126—and significant at the five percent level with robust
standard errors. In the insurgency and state violence equations, we again find positive and significant
27This estimation method requires several steps. First, a quasi-differentiation of the data is performed to eliminate all
individual effects. Second, the sample periods are truncated to ensure identifiability with lagged internal instruments. Third, the quasi-differenced model is multiplied by the matrix of instruments. Fourth, a generalized least-squares estima-tion is conducted. The variance-covariance matrix for the GLS step is estimated by using preliminary 2SLS estimates for each time period.
coefficients for a cycle of violence, i.e., mutual responses, at least at the five percent level. Specifically, the coefficients on State Violencet−1 are 0.136 and 0.0954 in Columns 2 and 5, respectively, and the
coefficients on Insurgencyt−1 are 0.252 and 0.215 in Columns 3 and 6, respectively. Moreover, these two variables have positive and significant AR(1) coefficients.
One should also wonder if the equations for different organizations in the same country could be further connected, for example, through systematic reaction rules of the state uniformly applied to all organizations or to coalitions of several organizations, or even substitutionality or complementarity relationships across organizations in the same country. However, our attempts to obtain such effects in our estimation trials led to insignificant results, perhaps partly because of the limited sample size within each country. Moreover, examining the strategy profiles of the organizations for each country, as inFigure I, does not seem to reveal blatant substitutions or complementarities across organizations. The estimates of the impulse response functions, displayed inFigure II, summarize the global dy-namic properties of the estimated system from Columns 4 to 6. The dashed lines indicate the 90 percent confidence bands. The considered shocks are 20 percent shifts in the probability of moving from peace to violence in terms of the examined strategy.
In the long run, e.g., after 10 years, all effects of the shocks are almost fully dampened. However, the mutual response between state violence and insurgency lasts longer than the consequences of other shocks. This persistence justifies qualifying this relationship as a (dampened) cycle of violence. This interpretation is also supported by the results of Granger causality tests based on the panel VAR estimates, which show that state violence causes insurgency and vice versa (p-values of 0.065 and 0.005, respectively).28
In the short run, these impacts peak after two years before dropping monotonically. Therefore, the responses of organizations last longer than what is directly suggested by examining only the es-timated coefficients for Insurgency and Terrorism. The dynamic interactions in the system maintain the heightened level of violence by organizations for a longer duration than what may have been their initial strategic intentions. In contrast, the horizon for terrorism seems to be very short. Panels 3 and 6 (Impulse: State Violence and Response: Terrorism and Insurgency, respectively) illustrate that the shock first increases organization violence, reaching its peak after two years and eventually subsiding. In contrast, Panels 7 and 8 (Impulse: Terrorism and Insurgency, respectively, and Response: State Vio-lence) display a continual dampening of the impact of the shock. The next subsection confirms these main results for a large variety of changes in data, specifications and estimation methods.
28We performed Granger causality tests based on the panel VAR estimates. These results support the choice of our main
variables and lag structure: ‘Terrorism’ is Granger caused by ‘Insurgency’ (p-value = 0.056, corresponding to the shift of violence); ‘State Violence’ causes ‘Insurgency’ with a p-value equal to 0.065, and ‘Insurgency’ causes ‘State Violence’ with a p-value equal to 0.005. These results are consistent with a dampened cycle of violence generated by violent responses originating in the violence of an opponent. These Granger causality tests do not inform us about causality per se but rather about the joint significance of the dynamic coefficients, and they do not solve the typical endogeneity problems. Even though the results support our analysis, we do not give them a central role, as they may not be robust to specification changes.
4.5
Robustness and extensions
The comparison of the FE and DGMM results shows that they produce effects that are almost always qualitatively similar, although the magnitudes of the response estimates with the DGMM are larger. An exception to this pattern is the significant (at the five percent level) negative response of terrorism to the one-year lag of state violence, which emerges in the DGMM results but not in the FE estimates. Other diverse estimation results, comparable to those shown inTable VandTable VI, are reported in the Online Appendix. They confirm those in the baseline tables. Specifically, in Table A1, we check for small-T sample bias by removing the organizations with short lifespans. This reduces the sample to 73 organizations. Nevertheless, the results are very similar to those ofTable Vregarding sign and significance.
We also include ethnicity×year fixed effects (instead of country×year fixed effects), as the data include ethnic minorities that are represented by several organizations in some countries. In Table A2, this allows for refined effects, such as the different treatment of distinct minorities by the state. The response of insurgency to state violence becomes insignificant at conventional levels, though still with positive estimated coefficients. However, accounting for the national conjuncture by using country×year fixed effects may seem more important.
We check the robustness of our results to the inclusion of additional diverse controls in Tables A3-A5. In Table A3, we add the controls ‘Illegal Organization’ to the estimations ofTable V. In Table A4, we add a control for non-lethal repression, i.e., ‘Ongoing Repression’, and in Table A5, we add controls for agreements, the implementation of agreements, and concessions. The construction of these controls is described in the Appendix. Their coefficients are typically insignificant, and their inclusion does not affect our main results.
In Table A6, we estimate a VAR(2) model with the eight variables used inTable Vand Tables A3-A5, i.e., Terrorism, Insurgency, State Violence, Illegal Organization, Ongoing Repression, Agreement, Implementation, and Concession. The main results are the same.
In Table A7, we use ordered logit fixed-effect models specifically designed for binary outcome variables (Baetschmann, Staub, and Winkelmann,2015). We find the same positive and significant responses to the violence of the opponent. In Table A8, we check that our results are not the conse-quence of outliers. The sample is restricted by removing the five percent of the organizations with the largest residuals in absolute value. The main results pass this test. In Table A9, we verify that the DGMM results are not affected by the simultaneous estimation of the country×year fixed effects, limited to those fixed effects that are significant at least at the 10 percent level in the FE estimation, which indicates that the preliminary purging of the country×year fixed effects is valid.
In Tables A10-A12, we perform estimations with different subsamples. We do not interpret these tables as robustness tests of our main results but rather as an exploration of the heterogeneity in the strategic cases. We limit the lag length of the model to one, and we consider only the fixed effect
estimator because these smaller samples constitute a statistical challenge due to the limited informa-tion available. Moreover, we restrict the sample to organizainforma-tions with a life span of at least 12 years to benefit from the square root of T-convergence. As a consequence, despite estimates that are often suggestive, it seems fair to say that the hazardous boundaries of an asymptotic statistical approach to these data are inspected here.
Table A10 contains the estimation results with country-specific samples for Iraq, Lebanon, and Israel, which are the countries with enough data and variation to yield useful estimates for each of the model coefficients. We find that, on average, organizations in Iraq respond significantly to state violence with insurgency. In contrast, in Israel and Lebanon, we do not find a systematic insurrection response to state violence among organizations, although the state responds violently to insurrection. This result is consistent with the results ofJaeger and Paserman(2006,2008).
In Table A11, we display minority-specific estimation results for samples of organizations rep-resenting the Kurds, Palestinians, Shi’a, and Sunnis in all the countries where they appear. All the main results are present again, although to varying degrees for each minority. We find a positive and significant response of insurgency to state violence for Shi’i organizations (Iraq, Lebanon, and Saudi Arabia). We also find a positive and significant statistical relationship between lagged terrorism and insurgency. For the Sunni organizations (Iran and Lebanon), we find a large positive and significant response of the state to insurgency, as opposed to the insignificant response for the Shi’a. The trans-fer of violence from insurgency to terrorism is not significant at conventional levels, despite the large magnitude of the estimated coefficient, probably due to the small sample sizes and the one-year lag re-striction. For the Palestinians in Israel, Jordan and Lebanon, we find a systematic terrorism response to state violence. For the Kurds in Iran, Iraq, and Turkey, we find a negative relationship between lagged terrorism and state violence.
In Table A12, we divide the sample according to the type of organization: religious, ethnic, or na-tionalist. Religious organizations are those that ‘advocate policies that incorporate religion into public life’, ethnic organizations are those which ‘have claims related to ethnicity but no claims to autonomy or independence’, and nationalist organizations are those which ‘have nationalist claims to autonomy or independence’. The category that displays the most significant effects is the one with the 46 eth-nic organizations. All the main effects are present, although sometimes only at the 10 percent level. Comparing the estimates of the non-religious vs. religious organization subsamples, we find a state response to insurgency for the non-religious organizations but not for the religious organizations. In the non-nationalist organization subsample, we observe a state response to both insurgency and terrorism, in contrast with the insignificant response of the state to the nationalist organizations. Fi-nally, there is some evidence of sequentiality from lagged terrorism to insurgency in the religious and non-nationalist subsamples.
In the next section, we supplement the raw discussion of the estimated correlations with strate-gic interpretations. Although this sort of commentary is common in narratives in the literature, we
propose a new method to lend it some formal justification. To do this, we now match the most salient empirical results, namely, the presence of state violence-insurgency cycles, with an analytical frame-work that we explore.
5
Matching the Empirical Results and the Analytical Framework
5.1
General principles
Our identification method is based on two features of the sixteen 2×2 one-shot normal form games inFigure III: (1) the Nash equilibria and (2) the preference ordering of each player as a function of each given decision of its opponent. When discussing the theory thus, we focus on analyzing the strategic relationship between state violence and insurgency. The case of terrorism is discussed in subsection 5.5.
By assuming a preference for nonviolence as a disambiguation device, sixteen separate types of strategic forms can be distinguished, which are the ones depicted inFigure III. These matrices repre-sent simultaneous-move games of two players, each of whom have two possible pure strategies, Peace or Violence. One player is the government (or ‘state’), which selects its strategy vertically on the ma-trix, while the second player is the organization, which chooses horizontally.29 Each square contains two ordinal payoffs corresponding to the state and the organization, respectively. The theoretical best responses of each player are indicated with thick arrows, and the Nash equilibria (NE) are encircled. Each best-response arrow shows the strategic choice of one player given the strategy chosen by the other player.
As mentioned before, we deliberately neglect potentially important elements of game theory mod-els such as information structures, beliefs, commitment issues, repeated games, the timing of deci-sions, long or infinite horizons, the selection of solution concepts, the aggregation of individual pref-erences within groups, negotiations and transfers across coalitions of agents, comparisons of military capacities, and other constraints. Indeed, these features of strategic conflicts are not observed pre-cisely for most of the state-organization pairs in the data used or in other databases that would cover all MENA countries. Such a dearth of data is acknowledged inAnderton and Carter(2009): “The
chal-lenge presented to social scientists when testing these models is that expectations and the private information on which they rest are unobservable”(p.89). Moreover, the identification conditions for sophisticated games
of incomplete information proposed in the theoretical literature are unlikely to be satisfied in typical data.30
Under these conditions, our parsimonious approach is useful. By design, we restrict the analysis
29We keep the convention of denoting the pair of strategies in the order State-Organization throughout.
30See, e.g.,de Paula and Tang,2012andAguirregabiria and Mira,2019. Finally,Salant and Cherry(2020) consider games
of the dynamic correlations among violent strategies to the simplest structural framework that can be elaborated from game theory while keeping open a priori the question of the involved strategic types. This is the data that will determine the most relevant strategy types, on average. Examining simple strategic patterns helps us to focus on a few fundamentals of conflict dynamics in a kind of theoretical reduced-form approach. In this framework, basic rationality hypotheses contribute to making sense of the observed violent dynamic responses of agents.
5.2
Matching estimates to Nash equilibria
The first stage of the analysis consists of matching the games inFigure IIIto the DGMM estimates by referring to Nash equilibria. There are several motivations for scanning the Nash equilibria. First, the common focus on Nash equilibria in the literature is already a device that is often used to avoid spec-ifying precise and arbitrary timing and procedures. Second, while there is no hope of being able to identify any complex model from the limited information available, Nash equilibria may be easier to diagnose. Third, there are theoretical reasons to believe that some outcomes of sophisticated games may often be indeterminate. For example, the folk theorem implies that subgame-perfect Nash equi-libria can generate almost any feasible and individually rational average payoffs in repeated games, provided that the discount factor tends to one. Therefore, restricting attention to Nash equilibria in basic one-shot games may assist in generating useful insights.
Moreover, there are observational and econometric reasons why the Nash equilibrium is an attrac-tive notion in our case. On the one hand, this view is consistent with many organizations never being observed in violent conflict against the state (listed in Table A13 in the Online Appendix), as would be the case if the Nash equilibrium is (Peace, Peace). On the other hand, stable situations, hence consis-tent with a Nash equilibrium from which no player has an incentive to deviate, can be well captured by fixed-effect components in panel models. One expects low (high) estimated fixed effects for the organizations that are never (always) observed as using and suffering violence.
Permanently peaceful cases occur for 57 out of the 110 organizations in the estimation sample. Compared to the average, the political orientation of these organizations leans democratic, often with leadership in the form of a council. Similarly, a few organizations are almost always observed fighting and being attacked by the state. These can be deemed to be firmly locked in a violent equilibrium. This is the case for the Partiya Karkari Kurdistan (PKK, Kurds, Example 3 in Table IV, Turkey), for both pairs of strategies State Violence-Insurgency and State Violence-Terrorism; the Supreme Council of the Islamic Revolution in Iraq (Example 7), for State Violence-Insurgency and prior to 1999 only; and Hamas (Example 15, Israel) for the strategy pair State Violence-Terrorism. Indeed, Panel 3 of
Figure Isuggests that the Turkish state and the PKK, a Kurdish party founded by Abdullah Ocalan in 1978 that at one point had over 30,000 fighters, stand in a violent equilibrium. In Panel 15, the state of Israel and the Palestinian party Hamas appear to be locked in a violent equilibrium characterized by terrorism. Hamas is a Sunni Islamist organization founded during the first Intifada in 1987. Its military
